Sample Paper – 2009
Class – X
Subject – Mathematics
Time-3hrs M.M.100
S-2
Section-A
1. Determine k so that 4k+8 , 2k2+3k+6 , 3k2+4k+4 are the three consecutive terms of an A.P.
2. Find a quadratic polynomial whose sum of the roots is Ö2 and product of the roots is 1/3
3. Two black queens are removed from 52 cards, find the probability of face card.
4. Find the distance between (a,b) and(-a,-b)
5. One end of the diameter of a circle is (2,3) and the center is (-2,5) find the co ordinates of the other end of the diameter.
6. Give an example of p (x) ,g(x) ,q(x) and r(x) which satisfies the division algorithm deg p(x)= deg q(x)
7. What is the nature of the roots of 2x2-5x+6
8. If tan A = 5/6 , find tha value of 1-Sec2A
9. State fundamental theorem of arithmetic.
10. Evaluate cosec2 36 –tan2 54
Section-B
11. How many terms of an AP are needed to give a sum of –25 the series is –6,-11/2,-5,…….
12. Show that cube of any positive integer is of the form 9m , 9m+1 or 9m+8 where m is some integer.
13. Prove that (1+cotA-cosecA)(1+tanA+secA)=2
14. Find the roots of 5x2-6x-2=0 by the method of completing the square
15. A die is thrown twice. What is the probability that (i)5 will not come up either time? (ii) 5 will come up at least once.
Section-C
16. Prove that the sum of the squares of the parallelogram is equal to the sum of the squares of its sides
17. If A( -2,-2) and B(2,-4) are points of the line segment AB ,find the co-ordinates of P lying on AB if AP=3/7AB.
18. If the roots of the equation (c2-ab)x2 –2(a2-bc)x +(b2 –ac) are equal ,prove that either a=0 or a3 +b3 +c3 =3abc .
19. The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house number x is equal to the sum of the numbers of the houses following it. Find the value of x.
20. (SinA-CosA+1)/(SinA+CosA-1)=1/ (SecA-TanA)
Or
If CosA-SinA+1 / CosA+SinA-1 = CosecA+CotA
21. If (1,2) ,(4,y),(x,6)and (2,-4) are the vertices of a parallelogram taken in order ,find the value of x and y.
22. Water flows at the rate of 10 m/min through a circular pipe of 5 mm diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
23. In the figure given below, two circles with centers A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region. (Take = 22/7).
24. Draw a Tr ABC in which AB=5cm and AC=4.3cm and Angle A=30o , Draw a Tr.BC’A’ similar to TrBCA such that BC’ :BC = 5:3
25. If the polynomial x4-6x3+16x2-25x+10 is divided by another polynomial x2-2x+k , the remainder comes out to be x+a , find the value of k and a
Section-D
26. The height of a cone is 30 cm . A small cone is cut off at the top by the plane parallel to the base. If its volume be 1/27 of the volume of the given cone , at what height above the base, the section has been made
27. Two lamp posts are of equal height. A boy standing mid way between them observes the elevation of the top of either post to be 400. after walking 15 m towards the towards one of them , he observes that the elevation of its top to be 60o. Find the height of the posts and the distance between them. Or
From a window P metres high above the ground of a house in a street, the angle of elevation and depression of the top and the foot of another house on opposite side of the street are α and β respectively. Show that the height of the opposite house is P(1+tanα)/tanβ.
28. A man walks a certain distance with acertain speed. If he walks ½ km/hr faster ,he takes 1 hr less. But if he walks 1 km/hr slower , he takes 3 more hrs. Find the distance traveled and his original speed of walking.
29. In a right triangle the square of the hypotenuse is equal to the square of the other two sides. In a Tr. ABC if ÐC =1200 , prove that AB2 = BC2 + CA2 + BC.CA
30. Marks obtained by 80 students are:
below 10- 3 , below 20- 8,below 30-15 ,below40-25,below50-37 ,below60-52,below70-64,below80-70,below90-80 and below100-85 ,calculate the median of the marks.
Paper Submitted by:
Vasudev
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Phone No. 9891884770
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